%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:55:17 AM UTC 2026
% Result : Unsatisfiable 3.82s 2.51s
% Output : Refutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 42 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 158 ( 18 ~; 16 |; 0 &; 124 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(g_decl,type,
g: $i ).
thf(h_decl,type,
h: $i ).
thf(codomain_decl,type,
codomain: $i > $i ).
thf(domain_decl,type,
domain: $i > $i ).
thf(compose_decl,type,
compose: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(1,negated_conjecture,
g != h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_g_equals_h) ).
thf(14,plain,
g != h,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
( ( h @ ( b @ compose ) )
= ( g @ ( b @ compose ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bh_equals_bg) ).
thf(44,plain,
( ( h @ ( b @ compose ) )
= ( g @ ( b @ compose ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ compose ) @ ( A @ compose ) )
= ( C @ ( B @ ( A @ compose ) @ compose ) ) )
| ( ( B @ codomain )
!= ( C @ domain ) )
| ( ( A @ codomain )
!= ( B @ domain ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_property) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ compose ) @ ( A @ compose ) )
= ( C @ ( B @ ( A @ compose ) @ compose ) ) )
| ( ( B @ codomain )
!= ( C @ domain ) )
| ( ( A @ codomain )
!= ( B @ domain ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ codomain @ domain )
= ( A @ codomain ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of_codomain_is_codomain) ).
thf(19,plain,
! [A: $i] :
( ( A @ codomain @ domain )
= ( A @ codomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
( ( b @ codomain )
= ( g @ domain ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_b_equals_domain_of_g) ).
thf(42,plain,
( ( b @ codomain )
= ( g @ domain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ compose ) @ domain )
= ( A @ domain ) )
| ( ( A @ codomain )
!= ( B @ domain ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_domain1) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ compose ) @ domain )
= ( A @ domain ) )
| ( ( A @ codomain )
!= ( B @ domain ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( A @ domain @ compose ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_composition) ).
thf(21,plain,
! [A: $i] :
( ( A @ ( A @ domain @ compose ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ compose ) @ codomain )
= ( B @ codomain ) )
| ( ( A @ codomain )
!= ( B @ domain ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_domain2) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ compose ) @ codomain )
= ( B @ codomain ) )
| ( ( A @ codomain )
!= ( B @ domain ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
( ( a @ codomain )
= ( b @ domain ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_b) ).
thf(38,plain,
( ( a @ codomain )
= ( b @ domain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( C @ ( b @ ( a @ compose ) @ compose ) )
!= B )
| ( ( b @ ( a @ compose ) @ codomain )
!= ( C @ domain ) )
| ( ( A @ ( b @ ( a @ compose ) @ compose ) )
!= B )
| ( ( b @ ( a @ compose ) @ codomain )
!= ( A @ domain ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',endomorphism) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( C @ ( b @ ( a @ compose ) @ compose ) )
!= B )
| ( ( b @ ( a @ compose ) @ codomain )
!= ( C @ domain ) )
| ( ( A @ ( b @ ( a @ compose ) @ compose ) )
!= B )
| ( ( b @ ( a @ compose ) @ codomain )
!= ( A @ domain ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ domain @ codomain )
= ( A @ domain ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_domain_is_domain) ).
thf(17,plain,
! [A: $i] :
( ( A @ domain @ codomain )
= ( A @ domain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
( ( b @ codomain )
= ( h @ domain ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_b_equals_domain_of_h) ).
thf(40,plain,
( ( b @ codomain )
= ( h @ domain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ codomain @ ( A @ compose ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_composition) ).
thf(23,plain,
! [A: $i] :
( ( A @ codomain @ ( A @ compose ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(74,plain,
$false,
inference(e,[status(thm)],[14,44,31,19,42,25,21,28,38,34,17,40,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n014.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 22:48:02 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.84/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/1.19 % [INFO] Parsing done (193ms).
% 1.33/1.21 % [INFO] Running in sequential loop mode.
% 1.89/1.60 % [INFO] eprover registered as external prover.
% 1.89/1.61 % [INFO] Scanning for conjecture ...
% 1.89/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.06/1.73 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.06/1.75 % [INFO] Problem is propositional (TPTP CNF).
% 2.06/1.76 % [INFO] Type checking passed.
% 2.06/1.77 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.82/2.51 % External prover 'e' found a proof!
% 3.82/2.51 % [INFO] Killing All external provers ...
% 3.82/2.51 % Time passed: 1956ms (effective reasoning time: 1295ms)
% 3.82/2.51 % Axioms used in derivation (12): codomain_of_a_equals_domain_of_b, bh_equals_bg, domain_of_codomain_is_codomain, codomain_composition, codomain_of_domain_is_domain, codomain_of_b_equals_domain_of_h, domain_composition, codomain_domain2, codomain_domain1, codomain_of_b_equals_domain_of_g, star_property, endomorphism
% 3.82/2.51 % No. of inferences in proof: 27
% 3.82/2.51 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1956 ms resp. 1295 ms w/o parsing
% 3.82/2.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.82/2.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------